One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics

Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-va...

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Autores principales: Franco, Eugenia, Gyllenberg, Mats, Diekmann, Odo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Netherlands 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8547227/
https://www.ncbi.nlm.nih.gov/pubmed/34720280
http://dx.doi.org/10.1007/s10440-021-00440-3
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author Franco, Eugenia
Gyllenberg, Mats
Diekmann, Odo
author_facet Franco, Eugenia
Gyllenberg, Mats
Diekmann, Odo
author_sort Franco, Eugenia
collection PubMed
description Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller’s classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived.
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spelling pubmed-85472272021-10-29 One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics Franco, Eugenia Gyllenberg, Mats Diekmann, Odo Acta Appl Math Article Despite their relevance in mathematical biology, there are, as yet, few general results about the asymptotic behaviour of measure valued solutions of renewal equations on the basis of assumptions concerning the kernel. We characterise, via their kernels, a class of renewal equations whose measure-valued solution can be expressed in terms of the solution of a scalar renewal equation. The asymptotic behaviour of the solution of the scalar renewal equation, is studied via Feller’s classical renewal theorem and, from it, the large time behaviour of the solution of the original renewal equation is derived. Springer Netherlands 2021-10-06 2021 /pmc/articles/PMC8547227/ /pubmed/34720280 http://dx.doi.org/10.1007/s10440-021-00440-3 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Franco, Eugenia
Gyllenberg, Mats
Diekmann, Odo
One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title_full One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title_fullStr One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title_full_unstemmed One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title_short One Dimensional Reduction of a Renewal Equation for a Measure-Valued Function of Time Describing Population Dynamics
title_sort one dimensional reduction of a renewal equation for a measure-valued function of time describing population dynamics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8547227/
https://www.ncbi.nlm.nih.gov/pubmed/34720280
http://dx.doi.org/10.1007/s10440-021-00440-3
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